Game cameras are rather inexpensive and are great for figuring out what is getting into your bird feeders overnight. Just set it up pointing at your feeder overnight, and you will have your answer the next day.
I had to modify a squirrel baffle on the pole to one of the bird feeders in order to keep the raccoons out of it. I didn't realize till I saw the captured images that they could just reach around the baffle, grab the pole above it, and pull themselves up and over it to get to the feeder.
So I had to modify the baffle a bit by putting something on top that extended a surface that the raccoons couldn't grab onto.
And that did the trick. They haven't been able to get into that feeder since the modification. So I have been able to retire the live trap.